2 In the Select physics tree, select AC/DC>Magnetic Fields (mf). ..... 1 In the Model Builder window, under Component 1>Mesh 1 right-click Free Tetrahedral.
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Magnetotellurics Introduction Magnetotellurics (MT) is a method for estimating the electric resistivity (or the reciprocal electrical conductivity) profile of the earth’s crust using the natural electromagnetic source provided by the ionosphere. The earth’s crust resistivity may vary over several orders of magnitude, and gives a strong indication to what kind of rocks are present. Metamorphic, igneous or sedimentary rocks might have resistivities varying from 0.1 to 105 Ωm, depending on several petrophysical parameters. The electromagnetic source in the MT method has its origin in the variations in the earth’s magnetic field, caused by solar wind and electromagnetic noise. These variations induce electric currents in the earth’s crust, proportional to the electrical conductivity. The electromagnetic source is random by nature, nevertheless, the low frequency signals and the shape of the ionosphere generate plane-wave components that can be correlated over large areas. By simultaneous measurements of the natural source electromagnetic field as function of time at different locations in an area of interest, one can statistically extract the local electromagnetic impedance as a function of frequency. This impedance can then be used to estimate the electric resistivity (or conductivity) as a function of depth. This model is inspired by a study published in 1997 (Ref. 1). In that article, various scientific groups compared software performance on few models. This model, called COMMEMI-3D-2, has become one of the benchmarks for MT modeling. I M P E D A N C E TE N S O R
MT analysis is based on the impedance tensor Z defined as E = Z⋅H
(1)
here, H is the magnetic field and E denotes the electric field. Normally, only the horizontal components of the fields are analyzed since the incident field is a plane-wave parallel to the earth’s surface. When the z-direction is the vertical axis, the relation for the horizontal components reads
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Ex Ey
=
Z xx Z xy H x Z yx Z yy H y
(2)
The impedance tensor’s components are then analyzed to determine the electric properties of the subsurface. For example, if the subsurface can be approximated with a 1D model (resistivity variations as a function of depth), the following relations follow: Z xx = Z yy = 0
(3)
Z xy = – Z yx
(4)
If the subsurface can be approximated with a 2D structure and the electric field is parallel to the strike (the axis in the horizontal plane along which the resistivity is constant), the mode is called transverse electric (TE). If the magnetic field is oriented along the strike, the mode is called transverse magnetic (TM). These two modes are uncoupled. Assuming that the x-axis is oriented along the strike, the impedance matrix component Zxy corresponds to the TE mode and Zyx describes the TM mode. In a 2D approximation, the impedance tensor’s components read Z xx = Z yy = 0
(5)
Z xy ≠ Z yx
(6)
and
In the general 3D case, the diagonal components Zxx and Zyy are different and non-zero. These diagonal matrix elements are often analyzed to determine the dimensionality of the subsurface. Traditionally, MT surveys are performed using electromagnetic sensors that are placed on the sea bottom or on land forming either lines or grids. The alignment of the sensors is often such that the line is perpendicular to the expected strike of the formation, such as a fault line. In a right-handed coordinate system with the z-axis points downwards from the surface of the model, the TE and TM modes relative to the coordinate system are then related to the impedance tensor, meaning that ZTE = Zxy and ZTM = Zyx. By positioning the sensors along a line perpendicular to the strike, the sensitivity is increased by measuring the biggest differences in induced currents across and parallel to the strike.
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APPARENT RESISTIVITY
When modeling MT with a know source, and the applied magnetic field is aligned along the y-axis, the apparent resistivity components are calculated from Ex 1 E 2 ρ xy = ------- ------x- , φ xy = arg ------- H y ωμ H y
(7)
Ey 1 E 2 ρ yy = ------- ------y- , φ yy = arg ------- H y ωμ H y
(8)
and the components in the impedance tensor read z xy = ρ xy e z yy = ρ yy e
iφ xy
(9)
iφ yy
(10)
Also, when the applied magnetic field is aligned along the x-axis, the apparent resistivity components are calculated from Ey 1 E 2 ρ yx = ------- ------y- , φ yx = arg ------- H x ωμ H x
(11)
Ex 1 E 2 ρ xx = ------- ------x- , φ xx = arg ------- H x ωμ H x
(12)
and the components of the impedance tensor read z yx = ρ yx e
iφ yx
z xx = ρ xx e
iφ xx
(13) (14)
Therefore, in order to determine all the components of the impedance tensor Z, two simulations must be run with two different field polarization.
Model Definition The geometry and parameters for this model are taken from Ref. 1. Two rectangular inserts of high conductivity are placed in the upper layer of a three-layer earth. The main idea of the study is to estimate those conductivities by the MT method.
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Figure 1: A 70 by 70 km piece of earth’s crust, consisting of three layers of different conductivities. From top to bottom, the conductivities are 10, 100 and 0.1 Ωm. The upper layer has two rectangular inserts of conductivities 1 and 100 Ωm. The model uses the Magnetic Fields physics in a 3D geometry. The magnetic field source is a plane wave that induces horizontal currents in the whole model. You impose periodic boundary conditions on the lateral sides to simulate an infinite domain. This assumption holds well if the domain is large enough around the area of interest. Make the computational domain larger if boundary effects are present. The imposed magnetic field is parallel to these boundaries. The magnetotellurics analysis is based on decomposition of the incoming plane waves into two waves with perpendicular polarizations. Hence, you solve these two polarizations in two independent physics interfaces. Then you solve the two physics interfaces in a single solver sequence to get all results in a single data set. The solutions from the two polarizations can thus be obtained by a parametric sweep for several frequencies.
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Results and Discussion The components of the apparent resistivity can now be extracted from the top layer of the model and plotted as surface plots for each frequency. This is where the measurements are made when real data are collected in magnetotelluric surveys. As discussed earlier, the apparent resistivity at certain position is equal to the resistivity below it in the case of a uniform half-space (1D model). Because the skin depth is small at high frequencies, the values of the apparent resistivity should be equal to the material resistivity in areas where a half-space approximation is valid. Indeed, that is what can be seen in Figure 2 and Figure 3. In the areas with uniform resistivities, far from the “fault lines,” the apparent resistivity is almost equal to the resistivity of the material right underneath. For a magnetotelluric survey the electromagnetic sensors are usually deployed along a line perpendicular to the expected fault line. Then, the apparent resistivity at a given frequency is plotted as a function of position along the line. See Figure 4 where data are extracted along a line crossing the three fault lines in the model. The results in this plot are comparable with the results published in the reference article (Ref. 1). At lower frequencies, the discrepancy between the apparent resistivity and the material resistivity values increases. Some magnetotellurics surveys also measure the z-component of the magnetic field. The plot of Hz is called the tipper plot. A rule of thumb is that a non-zero value of the tipper indicates a large change in resistivity from one side of a fault line to another. When moving along the direction of the field vector at a given phase value, the sign of the tipper indicates if one is moving from a region of higher resistivity to a low resistivity region (tipper is positive) or the opposite (tipper is negative). See Figure 6 where the tipper has been plotted on the domain, for the frequency of 0.01 Hz.
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Figure 2: Logarithm of apparent resistivity ρxy, top view of the 3D domain.
Figure 3: Logarithm of apparent resistivity ρyx, top view of the 3D domain.
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Figure 4: Apparent resistivity across strike(ρxy and ρyx), for the two frequencies 0.1 and 0.01 Hz.
Figure 5: Skin depth (m) at the center of the 3D model for the frequency of 0.01 Hz.
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Figure 6: Tipper plot, Hz component of magnetic field (A/m) for the frequency of 0.01 Hz. It is worth noting that magnetotelluric data analysis is typically done at frequencies ranging from 0.1 mHz to 10 Hz in an evenly spaced logarithmic scale. In this example, only two frequencies are modeled for simplicity. To calculate the response at other frequencies, the model should be adjusted by adapting the model size and the mesh accordingly. This is left as an exercise to the end user, but here are a few things to consider. For very high frequencies, the deep part of the model can be ignored. For low frequencies, the lateral dimensions should be larger. Evaluate the skin depth to be sure that the model is deep enough for the very low frequencies.
Reference 1. M. Zhdanov et al., “Methods for Modelling Electromagnetic Fields. Results from COMMEMI—The International Project on the Comparison of Modelling Methods for Electromagnetic Induction,” J. Appl. Geophys., vol. 37, pp. 133–271, 1997.
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Model Library path: ACDC_Module/Other_Industrial_Applications/ magnetotellurics
Modeling Instructions From the File menu, choose New. NEW
1 In the New window, click the Model Wizard button. MODEL WIZARD
1 In the Model Wizard window, click the 3D button. 2 In the Select physics tree, select AC/DC>Magnetic Fields (mf). 3 Click the Add button. 4 In the Select physics tree, select AC/DC>Magnetic Fields (mf). 5 Click the Add button. 6 Click the Study button. 7 In the tree, select Preset Studies for Selected Physics>Frequency Domain. 8 Click the Done button. GLOBAL DEFINITIONS
Parameters 1 On the Home toolbar, click Parameters.
The parameters Lx and Ly can be used to control the size of the domain to be studied. For the very low frequencies, these parameters may have to take values up to 100 km. For high frequencies, the domain can be much smaller. 2 In the Parameters settings window, locate the Parameters section. 3 In the table, enter the following settings: Name
Expression
Description
Lx
70[km]
Domain size in x direction
Ly
70[km]
Domain size in y direction
Lh
20[km]
Height of bottom layers
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Name
Expression
Description
h_box
10[km]
Box height
w_box
20[km]
Box width
d_box
40[km]
Box depth
GEOMETRY 1
Block 1 1 On the Geometry toolbar, click Block. 2 In the Block settings window, locate the Size section. 3 In the Width edit field, type Lx. 4 In the Depth edit field, type Ly. 5 In the Height edit field, type Lh. 6 Locate the Position section. From the Base list, choose Center. 7 In the z edit field, type -2*Lh. 8 Click the Build Selected button.
Block 2 1 On the Geometry toolbar, click Block. 2 In the Block settings window, locate the Size section. 3 In the Width edit field, type Lx. 4 In the Depth edit field, type Ly. 5 In the Height edit field, type Lh. 6 Locate the Position section. From the Base list, choose Center. 7 In the z edit field, type -Lh. 8 Click the Build Selected button. 9 Click the Go to Default 3D View button on the Graphics toolbar.
Block 3 1 On the Geometry toolbar, click Block. 2 In the Block settings window, locate the Size section. 3 In the Width edit field, type Lx. 4 In the Depth edit field, type Ly. 5 In the Height edit field, type h_box. 6 Locate the Position section. From the Base list, choose Center.
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7 In the z edit field, type -h_box/2. 8 Click the Build Selected button.
Block 4 1 On the Geometry toolbar, click Block. 2 In the Block settings window, locate the Size section. 3 In the Width edit field, type w_box. 4 In the Depth edit field, type d_box. 5 In the Height edit field, type h_box. 6 Locate the Position section. From the Base list, choose Center. 7 In the x edit field, type -w_box/2. 8 In the y edit field, type 0. 9 In the z edit field, type -h_box/2. 10 Click the Build Selected button.
Block 5 1 On the Geometry toolbar, click Block. 2 In the Block settings window, locate the Size section. 3 In the Width edit field, type w_box. 4 In the Depth edit field, type d_box. 5 In the Height edit field, type h_box. 6 Locate the Position section. From the Base list, choose Center. 7 In the x edit field, type w_box/2. 8 In the y edit field, type 0. 9 In the z edit field, type -h_box/2. 10 Click the Build Selected button. 11 Click the Go to Default 3D View button on the Graphics toolbar.
Form Union 1 In the Model Builder window, under Component 1>Geometry 1 right-click Form Union
and choose Build Selected. Now define the apparent resistivity variables.
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DEFINITIONS
Variables 1 1 In the Model Builder window, under Component 1 right-click Definitions and choose Variables. 2 In the Variables settings window, locate the Variables section. 3 In the table, enter the following settings: Name
Expression
Description
rho_xy
((abs(mf.Ex/mf.Hy))^2/ (2*pi*freq*mu0_const))
Apparent resistivity, xy
rho_yx
((abs(mf2.Ey/ mf2.Hx))^2/ (2*pi*freq*mu0_const))
Apparent resistivity, yx
rho_xx
((abs(mf2.Ex/ mf2.Hx))^2/ (2*pi*freq*mu0_const))
Apparent resistivity, xx
rho_yy
((abs(mf.Ey/mf.Hy))^2/ (2*pi*freq*mu0_const))
Apparent resistivity, yy
phi_xy
arg(1[S]*mf.Ex/ mf.Hy)[rad]+180[deg]
Apparent resistivity phase, xy
phi_yx
arg(1[S]*mf2.Ey/ mf2.Hx)[rad]+180[deg]
Apparent resistivity phase, yx
phi_xx
arg(1[S]*mf2.Ex/ mf2.Hx)[rad]+180[deg]
Apparent resistivity phase, xx
phi_yy
arg(1[S]*mf.Ey/ mf.Hy)[rad]+180[deg]
Apparent resistivity phase, yy
S
abs((mf2.Ex/ mf2.Hx+mf.Ey/mf.Hy)/ (mf.Ex/mf.Hy-mf2.Ey/ mf2.Hx))
Impedance skew
MATERIALS
Now define the four kinds of rock in this model. The relative permeability and permittivity are set to one. The resistivities, entered as conductivities, are 100, 10, 1 and 0.1 Ohm*m.
Material 1 1 On the Home toolbar, click New Material. 2 Select Domains 2 and 5 only. 3 In the Material settings window, locate the Material Contents section.
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4 In the table, enter the following settings: Property
Name
Value
Electrical conductivity
sigma
0.01
Relative permittivity
epsilonr
1
Relative permeability
mur
1
5 Right-click Component 1>Materials>Material 1 and choose Rename. 6 Go to the Rename Material dialog box and type Rock 100ohmm in the New name edit
field. 7 Click OK.
Material 2 1 On the Home toolbar, click New Material. 2 Select Domain 3 only. 3 In the Material settings window, locate the Material Contents section. 4 In the table, enter the following settings: Property
Name
Value
Electrical conductivity
sigma
0.1
Relative permittivity
epsilonr
1
Relative permeability
mur
1
5 Right-click Component 1>Materials>Material 2 and choose Rename. 6 Go to the Rename Material dialog box and type Rock 10ohmm in the New name edit
field. 7 Click OK.
Material 3 1 On the Home toolbar, click New Material. 2 Select Domain 4 only. 3 In the Material settings window, locate the Material Contents section. 4 In the table, enter the following settings: Property
Name
Value
Electrical conductivity
sigma
1
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Property
Name
Value
Relative permittivity
epsilonr
1
Relative permeability
mur
1
5 Right-click Component 1>Materials>Material 3 and choose Rename. 6 Go to the Rename Material dialog box and type Rock 1ohmm in the New name edit
field. 7 Click OK.
Material 4 1 On the Home toolbar, click New Material. 2 Select Domain 1 only. 3 In the Material settings window, locate the Material Contents section. 4 In the table, enter the following settings: Property
Name
Value
Electrical conductivity
sigma
10
Relative permittivity
epsilonr
1
Relative permeability
mur
1
5 Right-click Component 1>Materials>Material 4 and choose Rename. 6 Go to the Rename Material dialog box and type Rock 0.1ohmm in the New name edit
field. 7 Click OK. DEFINITIONS
Explicit 1 1 On the Definitions toolbar, click Explicit. 2 In the Explicit settings window, locate the Input Entities section. 3 From the Geometric entity level list, choose Boundary. 4 Select Boundaries 1, 4, 7, and 25–27 only. 5 Right-click Component 1>Definitions>Explicit 1 and choose Rename. 6 Go to the Rename Explicit dialog box and type x Boundaries in the New name edit
field. 7 Click OK.
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Explicit 2 1 On the Definitions toolbar, click Explicit. 2 In the Explicit settings window, locate the Input Entities section. 3 From the Geometric entity level list, choose Boundary. 4 Select Boundaries 2, 5, 8, and 11–13 only. 5 Right-click Component 1>Definitions>Explicit 2 and choose Rename. 6 Go to the Rename Explicit dialog box and type y Boundaries in the New name edit
field. 7 Click OK.
The following selections make it easier to set the boundary conditions later.
Explicit 3 1 On the Definitions toolbar, click Explicit. 2 In the Explicit settings window, locate the Input Entities section. 3 From the Geometric entity level list, choose Boundary. 4 Select Boundaries 10, 17, and 22 only. 5 Right-click Component 1>Definitions>Explicit 3 and choose Rename. 6 Go to the Rename Explicit dialog box and type Top in the New name edit field. 7 Click OK. MAGNETIC FIELDS
The magnetic field source is a plane wave that induces horizontal currents in the whole model. Impose periodic boundary conditions to make the domain look like an infinite domain. This assumption should hold well if the domain is large enough around the area of interest with 3D effects. Make Lx and Ly larger if the boundary effects are present. The imposed magnetic field should be parallel to these boundaries. The magnetotelluric analysis is based on decomposition of the incoming plane waves into two waves with perpendicular polarizations. Solve these two polarizations in two independent physics interfaces. Then solve the two physics interfaces in a single solver sequence to get all results in a single dataset. The solutions from the two polarizations can thus be obtained for several frequencies.
Periodic Condition 1 1 On the Physics toolbar, click Boundaries and choose Periodic Condition. 2 In the Periodic Condition settings window, locate the Boundary Selection section.
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3 From the Selection list, choose x Boundaries.
Use a Perfect Magnetic Conductor boundary condition to ensure that the magnetic field is perpendicular to these boundaries. For the other magnetic field polarization, the boundary conditions should be swapped.
Perfect Magnetic Conductor 1 1 On the Physics toolbar, click Boundaries and choose Perfect Magnetic Conductor. 2 In the Perfect Magnetic Conductor settings window, locate the Boundary Selection
section. 3 From the Selection list, choose y Boundaries.
The magnetic field is a plane wave with arbitrary amplitude and polarization along the x-axis or y-axis. For numerical stability, it makes sense to impose a magnetic field with a large amplitude. Because the magnetotelluric analysis is based on normalization between the various field components, the amplitude is not significant.
Magnetic Field 1 1 On the Physics toolbar, click Boundaries and choose Magnetic Field. 2 In the Magnetic Field settings window, locate the Boundary Selection section. 3 From the Selection list, choose Top. 4 Locate the Magnetic Field section. Specify the H0 vector as 0
x
1000
y
0
z
MAGNETIC FIELDS 2
Periodic Condition 1 1 On the Physics toolbar, from the Select Physics list (now showing Magnetic Fields),
choose Magnetic Fields 2. 2 On the Physics toolbar, click Boundaries and choose Periodic Condition. 3 In the Periodic Condition settings window, locate the Boundary Selection section. 4 From the Selection list, choose y Boundaries.
Perfect Magnetic Conductor 1 1 On the Physics toolbar, click Boundaries and choose Perfect Magnetic Conductor.
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2 In the Perfect Magnetic Conductor settings window, locate the Boundary Selection
section. 3 From the Selection list, choose x Boundaries.
Magnetic Field 1 1 On the Physics toolbar, click Boundaries and choose Magnetic Field. 2 In the Magnetic Field settings window, locate the Boundary Selection section. 3 From the Selection list, choose Top. 4 Locate the Magnetic Field section. Specify the H0 vector as 1000
x
0
y
0
z
Use mapped meshes in order to apply periodic boundaries. MESH 1
Free Triangular 1 1 In the Model Builder window, under Component 1 right-click Mesh 1 and choose More Operations>Free Triangular. 2 Select Boundaries 1, 2, 4, 5, 7, and 8 only. 3 Click the Build Selected button.
Copy Face 1 1 In the Model Builder window, right-click Mesh 1 and choose More Operations>Copy Face. 2 Select Boundaries 1, 4 and 7 only. 3 In the Copy Face settings window, locate the Destination Boundaries section. 4 Click the Active button to enable the selection of boundaries for the destination. 5 Select Boundaries 25, 26 and 27 only. MESH 1
Copy Face 2 1 In the Model Builder window, under Component 1 right-click Mesh 1 and choose More Operations>Copy Face. 2 Select Boundaries 2, 5 and 8only.
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3 In the Copy Face settings window, locate the Destination Boundaries section. 4 Click the Active button to enable the selection of boundaries for the destination. 5 Select Boundaries 11, 12 and 13 only.
The mesh must be adapted to the frequency. For high frequencies, the mesh must be fine, and the deeper parts of the model can be excluded from the active domains.
Free Tetrahedral 1 Right-click Mesh 1 and choose Free Tetrahedral.
Size 1 1 In the Model Builder window, under Component 1>Mesh 1 right-click Free Tetrahedral 1 and choose Size. 2 In the Size settings window, locate the Geometric Entity Selection section. 3 From the Geometric entity level list, choose Domain. 4 Select Domains 4 and 5 only. 5 Locate the Element Size section. From the Predefined list, choose Extra fine. 6 In the Settings window, click Build All. STUDY 1
Set the frequencies for which to solve; the low frequencies may take a long time to solve, and the mesh and the size of the domain should be adapted to each frequency.
Step 1: Frequency Domain 1 In the Model Builder window, expand the Study 1 node, then click Step 1: Frequency Domain. 2 In the Frequency Domain settings window, locate the Study Settings section. 3 In the Frequencies edit field, type 0.1 0.01.
To obtain separate solutions for the two polarizations, deactivate the second physics interface in the first solver step. 4 Locate the Physics and Variables Selection section. In the table, disable the Magnetic Fields 2 physics:
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Solve for
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Step 2: Frequency Domain 2 1 On the Study toolbar, click Study Steps and choose Frequency Domain>Frequency Domain. 2 In the Frequency Domain settings window, locate the Study Settings section. 3 In the Frequencies edit field, type 0.1 0.01.
Deactivate the first physics interface in the second solver step. 4 Locate the Physics and Variables Selection section. In the table, disable the Magnetic Fields physics: Physics
Solve for
Magnetic Fields
×
Solver 1 1 On the Study toolbar, click Show Default Solver. 2 In the Model Builder window, expand the Study 1>Solver Configurations node. 3 In the Model Builder window, expand the Solver 1 node, then click Dependent Variables 2. 4 In the Dependent Variables settings window, locate the General section. 5 From the Defined by study step list, choose User defined. 6 Locate the Initial Values of Variables Solved For section. From the Method list, choose Initial expression. 7 From the Solution list, choose Zero. 8 Locate the Values of Variables Not Solved For section. From the Selection list, choose All. 9 On the Study toolbar, click Compute. RESULTS
Data Sets 1 On the Results toolbar, click Cut Plane. 2 In the Cut Plane settings window, locate the Plane Data section. 3 From the Plane list, choose xy-planes.
2D Plot Group 3 1 On the Results toolbar, click 2D Plot Group. 2 On the 2D Plot Group 3 toolbar, click Surface.
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3 In the Surface settings window, locate the Expression section. 4 In the Expression edit field, type log10(rho_xy/1[ohmm]). 5 On the 2D Plot Group 3 toolbar, click Plot. 6 Click the Go to Default 3D View button on the Graphics toolbar. 7 In the Model Builder window, click 2D Plot Group 3. 8 In the 2D Plot Group settings window, click to expand the Title section. 9 From the Title type list, choose Manual. 10 In the Title text area, type Apparent resistivity, xy, log scale. 11 Right-click 2D Plot Group 3 and choose Rename. 12 Go to the Rename 2D Plot Group dialog box and type Apparent resistivity, xy
in the New name edit field. 13 Click OK.
2D Plot Group 4 1 On the Results toolbar, click 2D Plot Group. 2 On the 2D Plot Group 4 toolbar, click Surface. 3 In the Surface settings window, locate the Expression section. 4 In the Expression edit field, type log10(rho_yx/1[ohmm]). 5 In the Model Builder window, click 2D Plot Group 4. 6 In the 2D Plot Group settings window, click to expand the Title section. 7 From the Title type list, choose Manual. 8 In the Title text area, type Apparent resistivity, yx, log scale. 9 On the 2D Plot Group 4 toolbar, click Plot. 10 Right-click 2D Plot Group 4 and choose Rename. 11 Go to the Rename 2D Plot Group dialog box and type Apparent resistivity, yx
in the New name edit field. 12 Click OK.
Data Sets In this geometrically simple model, the strike is well known and the apparent resistivities can be plotted along a line crossing the strike. In the case of a half-space model, the apparent resistivity is equal to the resistivity of the half-space. The skin depth of the high-frequency waves is very short and the corresponding apparent resistivity will therefore be equal to the resistivity of the shallow features in the
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subsurface. The low frequencies will penetrate further and will "see" deeper into the Earth. Analysis of the apparent resistivity as a function of frequency is central to magnetotellurics and subsurface imaging can be done with inversion techniques using data from many frequencies over a large surface area. 1 On the Results toolbar, click Cut Line 3D. 2 In the Cut Line 3D settings window, locate the Line Data section. 3 In row Point 1, set x to -35000. 4 In row Point 2, set x to 35000.
1D Plot Group 5 1 On the Results toolbar, click 1D Plot Group. 2 In the 1D Plot Group settings window, locate the Data section. 3 From the Data set list, choose Cut Line 3D 1. 4 On the 1D Plot Group 5 toolbar, click Line Graph. 5 In the Line Graph settings window, click Replace Expression in the upper-right corner
of the y-axis data section. From the menu, choose Definitions>Apparent resistivity, xy (rho_xy). 6 Locate the x-Axis Data section. From the Parameter list, choose Expression. 7 Click Replace Expression in the upper-right corner of the x-axis data section. From
the menu, choose Geometry>Coordinate>x-coordinate (x). 8 Locate the x-Axis Data section. From the Unit list, choose km. 9 Click to expand the Legends section. Select the Show legends check box. 10 From the Legends list, choose Manual. 11 In the table, enter the following settings: Legends 0.1 Hz rho_xy 0.01 Hz rho_xy
12 On the 1D Plot Group 5 toolbar, click Plot. 13 Click the y-Axis Log Scale button on the Graphics toolbar. 14 Right-click Results>1D Plot Group 5>Line Graph 1 and choose Duplicate. 15 In the Line Graph settings window, click Replace Expression in the upper-right corner
of the y-axis data section. From the menu, choose Definitions>Apparent resistivity, yx (rho_yx).
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16 Locate the Legends section. In the table, enter the following settings: Legends 0.1 Hz rho_yx 0.01 Hz rho_yx
17 On the 1D Plot Group 5 toolbar, click Plot. 18 In the Model Builder window, right-click 1D Plot Group 5 and choose Rename. 19 Go to the Rename 1D Plot Group dialog box and type Apparent resistivity across strike in the New name edit field.
20 Click OK.
Magnetic Flux Density Norm (mf2) 1 In the Model Builder window, under Results>Magnetic Flux Density Norm (mf2)
right-click Multislice 1 and choose Delete. Click Yes to confirm. 2 In the Model Builder window, expand the Magnetic Flux Density Norm (mf2) node. 3 On the Magnetic Flux Density Norm (mf2) toolbar, click Slice. 4 In the Slice settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Magnetic Fields>Material properties>Skin depth (mf.deltaS). 5 Locate the Expression section. From the Unit list, choose km. 6 Locate the Plane Data section. From the Plane list, choose zx-planes. 7 In the Planes edit field, type 1. 8 In the Model Builder window, click Magnetic Flux Density Norm (mf2). 9 In the 3D Plot Group settings window, click to expand the Title section. 10 From the Title type list, choose Manual. 11 In the Title text area, type Skin depth. 12 On the Magnetic Flux Density Norm (mf2) toolbar, click Plot. 13 Right-click Magnetic Flux Density Norm (mf2) and choose Rename. 14 Go to the Rename 3D Plot Group dialog box and type Skin depth in the New name
edit field. 15 Click OK.
Magnetic Flux Density Norm (mf) 1 In the Model Builder window, expand the Results>Magnetic Flux Density Norm (mf)
node.
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2 Right-click Multislice 1 and choose Delete. 3 On the Magnetic Flux Density Norm (mf) toolbar, click Surface. 4 In the Surface settings window, click Replace Expression in the upper-right corner of
the Expression section. From the menu, choose Magnetic Fields>Magnetic>Magnetic field>Magnetic field, z component (mf.Hz). 5 In the Model Builder window, click Magnetic Flux Density Norm (mf). 6 In the 3D Plot Group settings window, click to expand the Title section. 7 From the Title type list, choose Manual. 8 In the Title text area, type Tipper, z component of H. 9 On the Magnetic Flux Density Norm (mf) toolbar, click Plot. 10 Right-click Magnetic Flux Density Norm (mf) and choose Rename. 11 Go to the Rename 3D Plot Group dialog box and type Tipper, z component of H
in the New name edit field. 12 Click OK.
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